Dual resonance in vortex-induced vibrations at subcritical and supercritical Reynolds numbers

An experimental study is performed on the vortex induced vibrations of a rigid flexibly mounted circular cylinder placed in a crossflow. The cylinder is allowed to oscillate in combined crossflow and in-line motions, and the ratio of the nominal in-line and transverse natural frequencies is varied systematically. Experiments were conducted on a smooth cylinder at subcritical Reynolds numbers between 15 000 and 60 000 and on a roughened cylinder at supercritical Reynolds numbers between 320 000 and 710 000, with a surface roughness equal to 0.23 % of the cylinder diameter. Strong qualitative and quantitative similarities between the subcritical and supercritical experiments are found, especially when the in-line natural frequency is close to twice the value of the crossflow natural frequency. In both Reynolds number regimes, the test cylinder may exhibit a ‘dual-resonant’ response, resulting in resonant crossflow motion at a frequency fv, near the Strouhal frequency, and resonant in-line motion at 2 fv. This dual resonance is shown to occur over a relatively wide frequency region around the Strouhal frequency, accompanied by stable, highly repeatable figure-eight cylinder orbits, as well as large third-harmonic components of the lift force. Under dual-resonance conditions, both the subcritical and the supercritical response is shown to collapse into a narrow parametric region in which the effective natural-frequency ratio is near the value 2, regardless of the nominal natural-frequency ratio. Some differences are noted in the magnitudes of forces and the cylinder response between the two different Reynolds number regimes, but the dual-resonant response and the resulting force trends are preserved despite the large Reynolds number difference.